Tabl. 8. The expansion of the money supply by a system of commercial banks

The money multiplier (m) shows the maximum amount of money, which can be created by one dollar of excess reserves, the required reserve ratio given. The money multiplier is Inversely proportional to the required reserve ratio, or

m = 1 / R, where

m – a money multiplier

R – a required reserve ratio

So we can see that the larger the required reserve ratio is the smaller the money multiplier is; the less money can be created and the less the money supply is.

Now suppose the commercial banking system has $1 million in cash and for strictly commercial purposes would normally maintain cash reserves equal to 5% of sight deposits. Since sight deposits will be 20 times cash reserves, the banking system will create $20 million of sight deposits against its $1 million cash reserves:

cash reserves $1 mln – 5%

sight deposits x – 100%

x == $1 mln x 100% : 5% = $20 mm.

Suppose the Bank now imposes a reserve requirement that banks must hold cash reserves of at least 10% of sight deposits. Now banks can create only $10 million sight deposits against their cash reserves of $1 million. Thus a reserve requirement acts like a tax on banks by forcing them to hold a higher fraction of their total assets as bank reserves and a lower fraction as loans earning high interest rates.

Thus, when the central bank imposes a reserve requirement in excess of the reserve ratio that prudent banks would anyway have maintained, the effect is to reduce the creation of bank deposits, reduce the value of the money multiplier, and reduce the money supply. Similarly, when a particular reserve requirement is already in force, any increase in the reserve requirement will reduce the money supply.